https://file.aiquickdraw.com/mathbot/file/1725891977386ytj9ur1t.jpg

Let's break down the math problem from the image.

We are given:
- Frederick and Kate have 17 1/3 cups of flour.
- Frederick's recipe calls for 1 3/4 cups of flour per loaf.
- Kate's recipe calls for 1 5/8 cups of flour per loaf.

We are tasked with determining the correct statements about the number of loaves each recipe can produce and how much flour will be left over.

### Step-by-Step Calculation:

1. **Total flour available**: 
   \[
   17 \frac{1}{3} = 17 + \frac{1}{3} = \frac{52}{3} \text{ cups of flour.}
   \]

2. **Flour per loaf for Frederick's recipe**:
   \[
   1 \frac{3}{4} = 1 + \frac{3}{4} = \frac{7}{4} \text{ cups per loaf.}
   \]

3. **Flour per loaf for Kate's recipe**:
   \[
   1 \frac{5}{8} = 1 + \frac{5}{8} = \frac{13}{8} \text{ cups per loaf.}
   \]

4. **Number of loaves Frederick can make**:
   \[
   \frac{52}{3} \div \frac{7}{4} = \frac{52}{3} \times \frac{4}{7} = \frac{208}{21} \approx 9.9 \text{ loaves (which rounds to 10 loaves).}
   \]

5. **Number of loaves Kate can make**:
   \[
   \frac{52}{3} \div \frac{13}{8} = \frac{52}{3} \times \frac{8}{13} = \frac{416}{39} \approx 10.67 \text{ loaves (which rounds to 11 loaves).}
   \]

6. **Leftover flour with Frederick's recipe**:
   - After making 10 loaves, Frederick would use \(10 \times \frac{7}{4} = \frac{70}{4} = 17.5\) cups of flour.
   - Leftover flour = \(17 \frac{1}{3} - 17.5 = \frac{52}{3} - \frac{35}{2} = \frac{104 - 105}{6} = -\frac{1}{6} \text{ cups (no flour left)}.\)

7. **Leftover flour with Kate's recipe**:
   - After making 11 loaves, Kate would use \(11 \times \frac{13}{8} = \frac{143}{8} = 17.875\) cups of flour.
   - Leftover flour = \(17 \frac{1}{3} - 17.875 = \frac{52}{3} - \frac{143}{8} = \frac{416 - 429}{24} = -\frac{13}{24} \text{ cups (again no flour left)}.\)

### Verifying the Statements:
- **Frederick's recipe will make 10 whole loaves** – TRUE.
- **Kate’s recipe will make 11 whole loaves** – TRUE.
- **There will be less flour left over if Frederick's recipe is used** – FALSE (both use almost all the flour, with no significant leftover).
- **There will be less flour left over if Kate's recipe is used** – FALSE.
- **More loaves of bread can be made using Kate’s recipe than Frederick's recipe** – TRUE.

Would you like more details or clarifications on any of the steps?

### Related Questions:
1. How would the number of loaves change if they had 20 cups of flour instead of 17 1/3?
2. What if Frederick's recipe used 2 cups of flour per loaf?
3. How much more efficient is Kate’s recipe compared to Frederick's in terms of flour usage?
4. What would happen if the total flour available was reduced to 15 cups?
5. Could Kate make half loaves if there was less flour available?

**Tip**: Always break down fractions into improper fractions for easier division!

Frederick and Kate have 17 1/3 cups of flour. Frederick's recipe calls for 1 3/4 cups of flour per loaf, and Kate's recipe calls for 1 5/8 cups of flour per loaf. How many whole loaves can each make and how much flour will be left over?

Learn how to calculate the number of whole loaves that can be made from a specific amount of flour using two different recipes, along with the flour that will be left over. This problem requires understanding of fraction operations and proportions.

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